A331305 -id:A331305 - cp's OEIS frontend

A331306 Lexicographically earliest infinite sequence such that a(i) = a(j) => A285732(i) = A285732(j) for all i, j.

1, 2, 2, 3, 4, 5, 6, 5, 3, 7, 8, 9, 10, 9, 11, 12, 13, 7, 6, 14, 15, 16, 17, 14, 18, 13, 19, 20, 21, 22, 23, 11, 8, 23, 24, 25, 26, 27, 28, 19, 29, 17, 30, 31, 32, 33, 34, 35, 30, 15, 12, 28, 36, 37, 38, 39, 40, 41, 42, 24, 43, 22, 42, 44, 45, 46, 47, 48, 49, 50, 36, 20, 16, 35, 51, 52, 53, 54, 55, 56, 57, 58, 51, 31, 59, 27, 50, 60, 61, 62, 63, 64, 65, 66, 67, 68, 44, 25, 21, 41

Offset: 1

Antti Karttunen, Jan 19 2020

Restricted growth sequence transform of A285732 (when considered as an one-dimensional sequence).
For all i, j:
  a(i) = a(j) => A003989(i) = A003989(j),
  a(i) = a(j) => A331307(i) = A331307(j) => A072030(i) = A072030(j).

Antti Karttunen, Table of n, a(n) for n = 1..25425

Cf. A003989, A072030, A285732.

Cf. also A331305, A331307.

up_to = 25425; \\ = binomial(225+1,2)
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A000027pairton(a,b) = ((2+((a+b)^2 - a) - (3*b))/2);
A285732sq(n, k) = if(n==k,-n,if(n>k,A000027pairton(n-k,k),A000027pairton(n,k-n)));
A285732list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A285732sq(col,(a-(col-1))))); (v); };
v331306 = rgs_transform(A285732list(up_to));
A331306(n) = v331306[n];

A331307 Lexicographically earliest infinite sequence such that for all i, j: a(i) = a(j) => f(i) = f(j), where f(n) = A285722(n), except f(1) = -1.

Original entry on oeis.org

1, 2, 2, 3, 4, 5, 6, 5, 3, 7, 8, 9, 4, 9, 10, 11, 12, 7, 6, 13, 14, 15, 16, 13, 4, 12, 17, 18, 19, 20, 21, 10, 8, 21, 22, 23, 24, 25, 26, 17, 4, 16, 27, 28, 29, 30, 31, 32, 27, 14, 11, 26, 33, 34, 35, 36, 37, 38, 39, 22, 4, 20, 39, 40, 41, 42, 43, 44, 45, 46, 33, 18, 15, 32, 47, 48, 49, 50, 51, 52, 53, 54, 47, 28, 4, 25, 46, 55, 56, 57, 58, 59, 60, 61, 62, 63, 40, 23, 19, 38

Offset: 1

Antti Karttunen, Jan 19 2020

Restricted growth sequence transform of function: f(1) = -1, and for n>1, f(n) = A285722(n), when the latter is considered as an one-dimensional sequence.
For all i, j:
  A331306(i) = A331306(j) => a(i) = a(j) => A072030(i) = A072030(j).

Antti Karttunen, Table of n, a(n) for n = 1..25425

Cf. A072030, A285722.

Cf. also A331305, A331306.

up_to = 25425; \\ = binomial(225+1,2)
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A000027pairton(a,b) = ((2+((a+b)^2 - a) - (3*b))/2);
A285722sq(n, k) = if(n==k,0,if(n>k,A000027pairton(n-k,k),A000027pairton(n,k-n)));
A285722list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A285722sq(col,(a-(col-1))))); (v); };
v285722 = A285722list(up_to);
A285722(n) = v285722[n];
A331307aux(n) = if(1==n,-n,A285722(n));
v331307 = rgs_transform(vector(up_to, n, A331307aux(n)));
A331307(n) = v331307[n];

cp's OEIS Frontend

A331306 Lexicographically earliest infinite sequence such that a(i) = a(j) => A285732(i) = A285732(j) for all i, j.

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